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<meta property="og:description" content="1.Give the three representations of an AND gate and say in your words what AND means. Ⅰ. Boolean expressions： Y = AB
Ⅱ. logic diagrams： Ⅲ. truth tables： 与门：当所有输入都为1是，输出才是1，否则输出0。
2.Give the three representations of an XOR gate and say in your words what XOR means. Ⅰ. Boolean expressions： Y = (¬XY)&#43;(X¬Y)
Ⅱ. logic diagrams： Ⅲ. truth tables： 异或门：当两个输入不相等时输出1，相等时输出0。
3.Draw a circuit diagram corresponding to the following Boolean expression: (A &#43; B)(B &#43; C) 4." />
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Ⅱ. logic diagrams： Ⅲ. truth tables： 与门：当所有输入都为1是，输出才是1，否则输出0。
2.Give the three representations of an XOR gate and say in your words what XOR means. Ⅰ. Boolean expressions： Y = (¬XY)&#43;(X¬Y)
Ⅱ. logic diagrams： Ⅲ. truth tables： 异或门：当两个输入不相等时输出1，相等时输出0。
3.Draw a circuit diagram corresponding to the following Boolean expression: (A &#43; B)(B &#43; C) 4.">
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<meta name="twitter:description" content="1.Give the three representations of an AND gate and say in your words what AND means. Ⅰ. Boolean expressions： Y = AB
Ⅱ. logic diagrams： Ⅲ. truth tables： 与门：当所有输入都为1是，输出才是1，否则输出0。
2.Give the three representations of an XOR gate and say in your words what XOR means. Ⅰ. Boolean expressions： Y = (¬XY)&#43;(X¬Y)
Ⅱ. logic diagrams： Ⅲ. truth tables： 异或门：当两个输入不相等时输出1，相等时输出0。
3.Draw a circuit diagram corresponding to the following Boolean expression: (A &#43; B)(B &#43; C) 4."/>

	
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      <h1 class="f1 athelas mt3 mb1">第五周作业</h1>
      
      
      <time class="f6 mv4 dib tracked" datetime="2020-10-03T21:33:11+08:00">October 3, 2020</time>

      
      
    </header>
    <div class="nested-copy-line-height lh-copy serif f4 nested-links nested-img mid-gray pr4-l w-two-thirds-l"><h2 id="1give-the-three-representations-of-an-and-gate-and-say-in-your-words-what-and-means">1.Give the three representations of an AND gate and say in your words what AND means.</h2>
<p>Ⅰ. Boolean expressions： Y = AB</p>
<p>Ⅱ. logic diagrams：
<img src="https://timgsa.baidu.com/timg?image&amp;quality=80&amp;size=b9999_10000&amp;sec=1601747150850&amp;di=b430b9c58b5e207c33b13360d85b6de2&amp;imgtype=0&amp;src=http%3A%2F%2Fimgsrc.baidu.com%2Fforum%2Fw%3D580%2Fsign%3D49c101145a82b2b7a79f39cc01accb0a%2Ffc453b5494eef01fd2ac81d5e3fe9925bd317db5.jpg" alt=""></p>
<p>Ⅲ. truth tables：
<img src="https://timgsa.baidu.com/timg?image&amp;quality=80&amp;size=b9999_10000&amp;sec=1601747271180&amp;di=92193222435e35f25e2c75ef7ab5a280&amp;imgtype=0&amp;src=http%3A%2F%2Fimg4.imgtn.bdimg.com%2Fit%2Fu%3D266356194%2C976381272%26fm%3D214%26gp%3D0.jpg" alt=""></p>
<p>与门：当所有输入都为1是，输出才是1，否则输出0。</p>
<h2 id="2give-the-three-representations-of-an-xor-gate-and-say-in-your-words-what-xor-means">2.Give the three representations of an XOR gate and say in your words what XOR means.</h2>
<p>Ⅰ. Boolean expressions： Y = (¬XY)+(X¬Y)</p>
<p>Ⅱ. logic diagrams：
<img src="https://timgsa.baidu.com/timg?image&amp;quality=80&amp;size=b9999_10000&amp;sec=1601747656737&amp;di=d758620020c43a016e04ca20fbaac8e4&amp;imgtype=0&amp;src=http%3A%2F%2Fgss0.baidu.com%2F7Po3dSag_xI4khGko9WTAnF6hhy%2Fzhidao%2Fpic%2Fitem%2F8718367adab44aed19715c8eb21c8701a18bfb99.jpg" alt=""></p>
<p>Ⅲ. truth tables：
<img src="https://timgsa.baidu.com/timg?image&amp;quality=80&amp;size=b9999_10000&amp;sec=1601747626841&amp;di=50b6bca9bba65962d415a197b7f172da&amp;imgtype=0&amp;src=http%3A%2F%2Fss.csdn.net%2Fp%3Fhttps%3A%2F%2Fmmbiz.qpic.cn%2Fmmbiz_jpg%2FldSjzkNDxllfCibxg8iamUs1Pb4JGyM4zRm6VniaA4BnLSuqic5pqgTBficZsavMEmq3K2Ba9AE8bibKmRgVvY3vFUfQ%2F640%3Fwx_fmt%3Djpeg" alt=""></p>
<p>异或门：当两个输入不相等时输出1，相等时输出0。</p>
<h2 id="3draw-a-circuit-diagram-corresponding-to-the-following-boolean-expression-a--bb--c">3.Draw a circuit diagram corresponding to the following Boolean expression: (A + B)(B + C)</h2>
<p><img src="../pic/53.png" alt=""></p>
<h2 id="4show-the-behavior-of-the-following-circuit-with-a-truth-table">4.Show the behavior of the following circuit with a truth table</h2>
<p><img src="../pic/54.png" alt=""></p>
<h2 id="5what-is-circuit-equivalence-use-truth-table-to-prove-thefollowing-formula">5.What is circuit equivalence? Use truth table to prove thefollowing formula.</h2>
<pre><code>            (AB)’ = A’ + B’
</code></pre>
<p>电路等效：两个电路虽然元件不同，但是逻辑效果是等价的，即在输入相同的情况下，两个电路输出的结果是一样的。</p>
<p><img src="../pic/551.png" alt=""></p>
<p><img src="../pic/552.png" alt=""></p>
<h2 id="6there-are-eight-1-bit-full-adder-integrated-circuits-combine-them-to-8bit-adder-circuit-using-the-following-box-diagram">6.There are eight 1 bit full adder integrated circuits. Combine them to 8bit adder circuit using the following box diagram.</h2>
<p><img src="../pic/56.png" alt=""></p>
<h2 id="7-logical-binary-operations-can-be-used-to-modify-bit-pattern-such-as-xsub8subxsub7subxsub6subxsub5subxsub4subxsub3subxsub2subxsub1subsub2sub-and-00001111sub2sub--0000xsub4subxsub3subxsub2subxsub1subsub2sub-we-called-that-00001111sub2sub-is-a-mask-which-only-makes-low-4-bits-to-work-fill-the-follow-expression">7. Logical binary operations can be used to modify bit pattern. Such as (X<sub>8</sub>X<sub>7</sub>X<sub>6</sub>X<sub>5</sub>X<sub>4</sub>X<sub>3</sub>X<sub>2</sub>X<sub>1</sub>)<sub>2</sub> and (00001111)<sub>2</sub> = (0000X<sub>4</sub>X<sub>3</sub>X<sub>2</sub>X<sub>1</sub>)<sub>2</sub> We called that (00001111)<sub>2</sub> is a mask which only makes low 4 bits to work. Fill the follow expression</h2>
<p>(1) (X<sub>8</sub>X<sub>7</sub>X<sub>6</sub>X<sub>5</sub>X<sub>4</sub>X<sub>3</sub>X<sub>2</sub>X<sub>1</sub>)<sub>2</sub> or (00001111)<sub>2</sub> = (X<sub>8</sub>X<sub>7</sub>X<sub>6</sub>X<sub>5</sub>1111)<sub>2</sub></p>
<p>(2) (X<sub>8</sub>X<sub>7</sub>X<sub>6</sub>X<sub>5</sub>X<sub>4</sub>X<sub>3</sub>X<sub>2</sub>X<sub>1</sub>)<sub>2</sub> xor (00001111)<sub>2</sub> = (X<sub>8</sub>X<sub>7</sub>X<sub>6</sub>X<sub>5</sub>notX<sub>4</sub>notX<sub>3</sub>notX<sub>2</sub>notX<sub>1</sub>)<sub>2</sub></p>
<p>(3) ((X<sub>8</sub>X<sub>7</sub>X<sub>6</sub>X<sub>5</sub>X<sub>4</sub>X<sub>3</sub>X<sub>2</sub>X<sub>1</sub>)<sub>2</sub> and (11110000)<sub>2</sub>) or (not (X<sub>8</sub>X<sub>7</sub>X<sub>6</sub>X<sub>5</sub>X<sub>4</sub>X<sub>3</sub>X<sub>2</sub>X<sub>1</sub>)<sub>2</sub> and (00001111)<sub>2</sub>) = (X<sub>8</sub>X<sub>7</sub>X<sub>6</sub>X<sub>5</sub>notX<sub>4</sub>notX<sub>3</sub>notX<sub>2</sub>notX<sub>1</sub>)<sub>2</sub></p>
<h2 id="logic-gatehttpsenwikipediaorgwikilogic_gate"><a href="https://en.wikipedia.org/wiki/Logic_gate">Logic gate</a></h2>
<p>A <strong>logic gate</strong> is an idealized or physical electronic device implementing a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has for instance zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device.</p>
<p><strong>Logic gates</strong> are primarily implemented using diodes or transistors acting as electronic switches, but can also be constructed using vacuum tubes, electromagnetic relays (relay logic), fluidic logic, pneumatic logic, optics, molecules, or even mechanical elements. With amplification, logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic, and therefore, all of the algorithms and mathematics that can be described with Boolean logic.</p>
<h2 id="boolean-algebrahttpsenwikipediaorgwikiboolean_algebra"><a href="https://en.wikipedia.org/wiki/Boolean_algebra">Boolean algebra</a></h2>
<p>In mathematics and mathematical logic, <strong>Boolean algebra</strong> is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0, respectively. Instead of elementary algebra, where the values of the variables are numbers and the prime operations are addition and multiplication, the main operations of Boolean algebra are the conjunction (and) denoted as ∧, the disjunction (or) denoted as ∨, and the negation (not) denoted as ¬. It is thus a formalism for describing logical operations, in the same way that elementary algebra describes numerical operations.</p>
<h2 id="flip-flophttpszhwikipediaorgwikie8a7a6e58f91e599a8"><a href="https://zh.wikipedia.org/wiki/%E8%A7%A6%E5%8F%91%E5%99%A8">Flip-flop</a></h2>
<p><strong>触发器</strong>，是一种具有两种稳态的用于储存的组件，可记录二进制数字信号“1”和“0”。触发器是一种双稳态多谐振荡器（bistable multivibrator）。该电路可以通过一个或多个施加在控制输入端的信号来改变自身的状态，并会有1个或2个输出。触发器是构成时序逻辑电路以及各种复杂数字系统的基本逻辑单元。触发器和锁存器是在计算机、通讯和许多其他类型的系统中使用的数字电子系统的基本组成部分。</p>
<h3 id="1flip-flop-中文翻译是">1)Flip-flop 中文翻译是？</h3>
<p>触发器。</p>
<h3 id="2how-many-bits-information-does-a-sr-latch-store">2)How many bits information does a SR latch store?</h3>
<p>1 。</p>
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